LEARNING OBJECTIVESLEARNING OBJECTIVESBe able to recognize two-force Be able to recognize two-force membersmembersBe able to apply equations of Be able to apply equations of equilibrium to solve for unknownsequilibrium to solve for unknowns

RIGID BODY EQUILIBRIUM 2 - DRIGID BODY EQUILIBRIUM 2 - DIn 2-D, a body is in equilibrium if and only if the sum of In 2-D, a body is in equilibrium if and only if the sum of the forces in each direction is equal to zero and the sum the forces in each direction is equal to zero and the sum of the moment at any point is equal to zero.of the moment at any point is equal to zero.∑∑∑===0.0MFFYX

STEPS FOR SOLVING 2-D EQUILIBRIUM PROBLEMS1.Establish a suitable x-y coordinate system (if not given).2.Draw a free body diagram (FBD) of the object under analysis.3. Apply the three equations of equilibrium to solve for the unknowns.

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IMPORTANT NOTES1.If we have more unknowns than the number of independent equations then the problem is a statically indeterminate. We cannot solve this problem using just static.2. The order in which we apply equations may affect the simplicity of the solution. For example, if we have two unknown vertical forces and one unknown horizontal force, then solve for the horizontal force first using ∑FX= 0.3. If the answer for an unknown comes out as negative number then the direction of the unknown force is opposite to that drawn on the FBD.

APPLICATIONSFor a given load on the platform, how can we determine the forces at joint A and the force in the link (cylinder) BC?A steel beam is used to support roof joists. How can we determine the support reactions at each end of the beam?

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TWO-FORCE MEMBERSThe solution of some equilibrium problems can be simplified if we can recognize members that are subjected to forces at only two points (e.g., at points A and B).Applying the equations of equilibrium to such member one can determine the resultant forces at A and B. These resultants must be equal in magnitude and act in the opposite directions along the line joining points A and B.

EXAMPLE Two-force MembersIn the above figures, since the directions of the resultant forces at A and B are known (along the line joining points A and B), all AB members can be considered two-force members if their weights are neglected. This simplifies the equilibrium analysis of some rigid bodies.

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